Answer to Question #295393 in Algebra for Math assignment

Question

16. Solve in |R:

(a) 2(3y-2)+3(4-3y)>12-(5y+7)

(b) 2(k+2)+3(2k-3)<or=2

17.(a) if x=1-3t and y=2t-1.

Find the value of t such that x=y.

(b) solve for real value of x the equation,

(m+1)x²-(m+3)x+3-m=0.

When m=-1.

18.Given the parametric equations:

x=t-1/t

y=2(t+2)/t²

Find the coordinates of the point where,

(a) t=-2

(b) t=-1

19.solve in |R:

(a) 4(m+5)-6(2m+3)=3(m+14)-2(5-m)+9

(b) 3(k-1)-4(k+6)=10(k+5)

Answer 1

16.

a)

$$2(3y-2)+3(4-3y)>12-(5y+7)$$

$$6y-4+12-9y-12+5y+7>0$$

$$2y+3>0$$

$$y>-3/2$$

(b)

$$2(k+2)+3(2k-3)\le2$$

$$2k+4+6k-9\le 2$$

$$8k\le7$$

$$k\le7/8$$

17.

(a)

$$x=y=>1-3t =2t-1.$$

$$5t=2$$

$$t=2/5$$

(b)

$$(-1+1)x^2-(-1+3)x+3-(-1)=0$$

$$-2x+4=0$$

$$2x=4$$

$$x=2$$

18.

(a)

$$x=-2-1/(-2)=-3/2$$

$$y=2(-2+2)/(-2)^2=0$$

Point $(-3/2, 0)$

(b)

$$x=-1-1/(-1)=0$$

$$y=2(-1+2)/(-1)^2=2$$

Point $(0, 2)$

19.

(a)

$$4(m+5)-6(2m+3)=3(m+14)-2(5-m)+9$$

$$4m+20-12m-18=3m+42-10+2m+9$$

$$-8m+2=5m+41$$

$$13m=-39$$

$$m=-3$$

(b)

$$3(k-1)-4(k+6)=10(k+5)$$

$$3k-3-4k-24=10k+50$$

$$-k-27=10k+50$$

$$11k=-77$$

$$k=-7$$